The Commission on International Eclairage (CIE) recommended the CIELUV (or CIE L*u*v*) and CIELAB (or CIE L*a*b*) color spaces and their corresponding color difference formulas in 1976. The CIE L*a*b* color space and the CIE L*a*b* color formula are widely used in color imaging applications.
The CIE L*a*b* system describes and orders colors based on the opponent theory of color vision. The opponent theory states that colors are not able to be perceived as both red and green at the same time, nor yellow and blue at the same time. However, colors are able to be perceived as combinations of: red and yellow, red and blue, green and yellow, and green and blue.
CIE L*a*b* is a color model used to describe all of the colors visible to the human eye. The first of the three parameters in the model represents the luminance or lightness, L*, of the color wherein L*=0 indicates black and L*=100 indicates white. The position between red and green is indicated by a* wherein negative values indicate green and positive values indicate red. The position between blue and yellow is indicated by b* wherein negative values indicate blue and positive values indicate yellow.
CIE L*a*b* color difference, between any two colors in CIE 1976 color space, is the distance between the color locations. This distance is typically expressed as ΔE, where:ΔE=√{square root over ((ΔL*)2+(Δa*)2+(Δb*)2)}{square root over ((ΔL*)2+(Δa*)2+(Δb*)2)}{square root over ((ΔL*)2+(Δa*)2+(Δb*)2)}The chroma and hue angle are computed from the CIE L*a*b* space by the formula:C=√{square root over (a*2+b*2)}h=arc tan(b*/a*)While the color difference formula is widely used, its chroma scale is known to be fairly nonlinear.In 1994, CIE recommended an updated color difference formula named CIE 94, which is calculated from ΔL*ab, ΔC*ab and ΔH*ab:
      Δ    ⁢                  ⁢          E      94        =                              (                                    Δ              ⁢                                                          ⁢                              L                *                                                                    k                l                            ·                              S                l                                              )                2            +                        (                                    Δ              ⁢                                                          ⁢                              C                *                                                                    k                c                            ·                              S                c                                              )                2            +                        (                                    Δ              ⁢                                                          ⁢                              H                *                                                                    k                h                            ·                              S                h                                              )                2            where Sl=1, Sc=1+0.045 C*, Sh=1+0.015 C*kl, kc and kh are numeric parametric factors that permit the independent weighting of lightness (ΔL*ab), chroma (ΔC*ab) and hue (ΔH*ab) differences. Values selected for the parametric factors are shown in the naming convention CIE94 (kll:kc:kh).Another formula, the CMC Color difference formula is mainly used in the textile industry:
      Δ    ⁢                  ⁢          E      CMC        =                              (                                    Δ              ⁢                                                          ⁢                              L                *                                                    l              ·                              S                l                                              )                2            +                        (                                    Δ              ⁢                                                          ⁢                              C                *                                                    c              ·                              S                c                                              )                2            +                        (                                    Δ              ⁢                                                          ⁢                              H                *                                                    S              h                                )                2            Sl, Sc and Sh are CMC weighting functions that adjust the CIE differences (ΔL*ab, ΔC*ab and ΔH*ab) depending upon the location of the standard in CIE L*a*b* 1976 color space.
A user of the CMC formula usually sets values for l and c parameters according to practice in the industry. The numeric parametric factors, l and c, permit the independent weighting of lightness (ΔL*ab) and chroma (ΔC*ab) differences, relative to the hue (ΔH*ab) difference. Current practice is that c is set to 1 for all industries. And l is set to 2 for textiles and to about 1.4 for paint and plastics applications.
There are a number of image processing operations that are subject to halo artifacts across the edges. Halo artifacts are characterized by overestimation (“overshoot”) on one side of the edge and underestimation (“undershoot”) on the other side of the edge. FIG. 6A illustrates an unprocessed image, while FIG. 6B illustrates a halo artifact in the processed image. Most common image processing methods that generate halo artifacts are high dynamic range compression methods which rely on Gaussian style blurring, for example retinex, local color correction and iCam. Other common methods that generate halo artifacts are edge enhancement methods which include unsharp masking and Wallis Filter [statistical differencing].